On The Requirements of SAR Processing for Airborne Differential ...
On The Requirements of SAR Processing for Airborne Differential Interferometry Karlus A. C. de Macedo, Christian Andres and Rolf Scheiber Microwaves and Radar Institute German Aerospace Center (DLR) P.O. Box 1116, D-82234, Oberpfaffenhopfen, Germany Email: [karlus.macedo, christian.andres, rolf.scheiber]@dlr.de
Abstract— Airborne Differential SAR Interferometry (DInSAR) is still a challenging task when compared to the spaceborne case due to the fact that airborne platforms are unable to describe a stable flight track. For that reason a very precise motion compensation which includes the correction of topographic-induced phase errors has to be performed in the airborne SAR data. This paper presents the required steps of phase correction to achieve accurate airborne D-InSAR data. The latest airborne D-InSAR processing chain of the E-SAR system is shown. Differential interferograms results using the proposed processing chain are also shown.
I. I NTRODUCTION Differential Interferometry using Synthetic Aperture Radar, D-InSAR, is a technique to measure movements of the Earth’s surface at sub-wavelength scale. The D-InSAR technique uses the interferometric phases to measure the changes in the pathlength between two acquisition times. The interferometric phase between two SAR images taken at different times and from different positions can be expressed as (repeat-pass interferometry): φint = φtopo + φf e + φdif f ,
(1)
where φtopo denotes the phase contribution caused by terrain topography, φf e the systematic phase corresponding to the flat Earth, and φdif f the differential phase corresponding to the changes of the path-length. The differential phase, φdif f , is estimated by compensating the phase contributions due to topography and flat Earth by using a DEM (Digital Elevation Model)or/and a second interferometric phase without differential effect (very short temporal baseline). The accuracy of the D-InSAR measurements, φdif f , can be affected by atmospheric conditions, deviations of the platform from the nominal track, and noise contributions due to low SNR, baseline and temporal decorrelations. The Differential phase can be writen as: φdif f = φn + φatm + φ∆topo + φ∆dev ,
(2)
where φn denotes the noise contribution φatm the phase contribution due to changes in atmospheric conditions, φ∆topo the phase changes in the path length due to the changes of the terrain surface, and φ∆dev the difference between the phase errors due to the different deviations of the sensor at different acquisition times. 0-7803-9050-4/05/$20.00 ©2005 IEEE.
Using space-borne SAR sensors, differential interferometry with sub-wavelength accuracy can be achieved [1], [2]. Although often very efficient due to the very stable platform track, the use of space-borne SAR has some drawbacks like phase artefacts caused by atmospheric effects, and low coherent data due to long time acquisition intervals. Due to the great flexibility of airborne sensors, temporal decorrelations can be kept in reasonable levels by using small temporal baselines. The effects caused by the atmosphere is small because of the fact that the area imaged by the airborne radar signal is small and no significant variations of the atmosphere take place. For airborne case the accuracy of the D-InSAR measurements are mainly affected by the deviations of the platform from the nominal track. These deviations cause phase errors in the SAR image making airborne D-InSAR very difficult. Efforts to make airborne D-InSAR measurements efficient and accurate have been made in the past years, with the accuracy improvement of the navigation systems and motion compensation (MoComp) approaches [3], [4], [5], [6]. This paper describes the required steps and their importance in order to perform airborne differential interferometry. In section II, the paper explains briefly the origin and effects of phase errors due to motion deviations. In section III, the paper presents the required steps for differential interferometry together with the latest airborne D-InSAR processing chain of the E-SAR system. Section IV shows the differential inteferometry results obtained using the presented processing chain. In section V, we address the conclusions. II. O RIGIN AND E FFECTS OF P HASE E RRORS DUE TO M OTION D EVIATIONS The SAR raw data are processed as if they were acquired on straight rectilinear tracks. This assumption is not met with airborne platform as motion deviations (motion errors) of the sensor platform from the rectilinear (nominal) track can occur, causing phase errors both in range and azimuth. For a single SAR acquisition, the phase error due to these deviations, φdev , is proportional to the difference between the nominal and real path-length distance ∆r: 4π φdev = ∆r, (3) λ where λ is the wavelength of the radar signal.
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Fig. 2.
Fig. 1.
D-InSAR processing chain.
The phase error φdev is topography- and aperture-dependent [6]. In broadside direction (zero Doppler) φdev0 , is given by: 4π (h + ∆z)2 + ( r02 − h2 + ∆y)2 , (4) φdev0 (r, x, h) = λ where h is the target height, ∆r0 is the difference between the nominal and real path-length in broadside direction, r0 is the closest range between the SAR and the target, ∆y and ∆z are the deviations in the horizontal and in the vertical directions obtained from navigation system measurements, and r and x are the variables for range and azimuth positions respectively. The effects of motion errors are summarized in [6] A non-linear phase error causes phase offset (first order effect), shift of the SAR impulse response function (IRF) from the nominal position (second order effect) and defocusing (high order effects). For airborne differential SAR interferometry (repeat-pass) processing, a very accurate motion compensation, along the whole synthetic aperture, to correct the phase of each single pass data is neeed. This is because the deviations of two acquisition times may significantly differ causing mismatch and phase error in the repeat-pass interferograms. Using very precise motion compensation, the phase errors in a SAR image can be corrected to the level of accuracy of the navigation system and the external DEM used. The remaining (residual) motion error can be estimated using approaches as described in [4], [7]. The next section shows the required steps and the latest approaches of phase correction to achieve airborne D-InSAR data with sub-wavelength accuracy. Fig. 1 shows the block diagram for the D-InSAR processing chain. III. A IRBORNE D-I N SAR P ROCESSING C HAIN A. Motion Compensation The first requirement towards accurate D-InSAR data is to compensate all motion errors that are computable for each single data acquisition. As described in section II, the phase error is topography-dependent and due to the large variations 0-7803-9050-4/05/$20.00 ©2005 IEEE.
Phase error as function of the topography variation.
of incidence angle in airborne geometry, the MoComp approach for airborne SAR must correct the phase error taking into consideration the DEM of the imaged scene. Fig. 2 shows, for L-band, that difference of 10 meters or more between the height and the DEM used can introduce phase errors up to a 100 degrees for 10m deviation. To perform motion compensation of phase errors, the processing chain of the E-SAR airborne system first compensates the phase error assuming a flat terrain. This is performed within Extended Chirp Scaling (ECS) algorithm in a two step process [3]. Rough range invariant compensation is performed at raw data stage, whereas precise range dependent MoComp is included after RCMC (range cell migration correction) just prior to azimuth compression. This compensation methodology is very precise for flat terrain and for resolutions in the order of one meter. The previous approach is unable to perform a Topographyand Aperture-Dependent Motion Compensation due to the superposition of the synthetic aperture of several targets having different topographic heights. Thus, after the previous compensation, the topography- and aperture-dependent phase errors must be computed using a DEM. This remaining (or residual) phase error is then corrected using the so called PTA-MoComp (Precise Topography- and Aperture-Dependent Motion Compensation) [6]. The PTA-MoComp approach is a FFT-based post-processing algorithm capable of compensating the high-order effects due to the topography and due to the angular-variation (Dopplervariation) along the synthetic aperture. The resulting motion compensation after applying PTA-MoComp is very precise. The limit relies on the accuracy of the adopted navigation system and the DEM used. B. Residual Motion Errors Estimation and Compensation Due to the limit of accuracy of the adopted navigation system, there are still phase errors in the image that we are not able to compute. These residual motion errors shall be estimated. Let φres1 and φres2 be the phase contribution for the residual motion errors of two SAR images. For the ESAR navigation system, measurement errors in the order of centimeters are expected, leading up to hundreds of degrees of phase errors in L-Band. The method used to estimate residual motion errors in the ESAR airborne repeat-pass (differential interferometry) data is based on the multisquint approach [4]. This method estimates
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Fig. 3.
Estimated ∆φres phase error.
Fig. 4. Differential Equation Error as function of the topography variation (independent of wavelength).
the phase difference ∆φres between φres1 and φres2 , i.e. the residual motion errors in the interferogram. The ∆φres can be estimated by splitting the bandwidth of two SAR complex images S1 , S2 , building the interferograms of each subaperture A and B, and integrating their difference phase [4], [8]. The estimated ∆φres is then given by: ∆φres = arg [S1A S2A∗ (S1B S2B∗ )∗ ]dx + C, (5) where C is a unknown constant. The estimated ∆φres phase error can be converted into baseline deviations according to (right side-look geometry): λ = ∆By · cos (D ) − ∆Bz · sin (D ) , (6) 4π where D denotes the incidence angle, ∆By and ∆Bz the baseline errors in horizontal and vertical direction. Since the above method estimates the difference from the residual phase errors, we compensate the D-InSAR data by subtracting from the short- and long-term interferograms their corresponding estimated ∆φres phase error, followed by a pixel-by-pixel coregistration of the interferograms. Fig. 3 shows the estimated phase error ∆φres for the shortand long-term interferograms at near- and far-range for the D-InSAR data that will be shown in section IV. Due to the unknown constant in (5), an unknown baseline offset is presented in the interferometric data. Thus, a phase trend in range is to be expected. To compensate for this effect we compute the residual short- amd long-term interferograms, i.e., the short- and long-term inteferograms minus the interferometric phase derived from the DEM. Then, we take the range profiles of each residual interferograms and fit them to a quadratic function. The obtained phase trend is then inserted in (6) and the baseline offsets for each inteferogram are estimated in a least square sense. ∆φres
C. Generation of Differential Interferograms Even for ideal motion compensation or SAR images free of phase errors, special care has to be taken in order to generate airborne differential interferograms. The standard phase scaling approach to estimate the differential phase is given by [9]: Bl cos(θ0 − αl ) φints , φˆdif f,0 = φintl − Bs cos(θ0 − αs ) 0-7803-9050-4/05/$20.00 ©2005 IEEE.
(7)
where φints is the unwrapped short-term interferogram, φintl is the unwrapped long-term interferogram, αs is the tilt angle of the baseline for the short-term interferogram, αl is the tilt angle of the baseline for the long-term interferogram, Bs is the baseline length for the short-term interferogram, Bl is the baseline length for the long-term interferogram, θ0 is the look angle for the flat Earth. Due to the first order approximation around the look angle for the flat Earth involved in the derivation of (7), an error will appear when θ0 deviates from the real look angle, θtopo , which depends on the topography. For airborne geometry, the assumption of flat Earth during phase scaling leads to significant errors. Thus, the topography information must also be used to compute the airborne differential interferograms. Fig. 4 shows the error involved in the differential equation as a function of the topography. To obtain more accurate differential interferograms free of such phase errors, [10] reformulates the phase scaling and subtraction approach using an external DEM and 3 SAR data acquisition to form the short- and long-term interferograms. The estimation of the differential phase becomes [10]: Bl cos(θtopo − αl ) φresints , φˆdif f,topo = φresintl − Bs cos(θtopo − αs )
(8)
where φresints is the unwrapped residual short-term interferogram, φresintl is the unwrapped residual long-term interferogram θtopo is the look angle as function of the DEM. The differential interferograms of the E-SAR system are generated using (8). The error of the differential equation will be limited to the accuracy of the DEM used, which is is now the reference level in a pixel-by-pixel basis. In Fig. 4, we see that a 20m accurate DEM is enough for differential equation error lower than 1.0mm with 5m baseline interferograms. The phase of the residual interfrograms have mainly the contributions due to the surface movement, DEM error noise due to decorrelation effects and residual phase errors. If these contributions are negligible and the residual short-term interferogram phase φresint1 is limited to a phase cycle [−π, π) then, there is no need of unwrapping prior to phase scaling. The displacement map of the surface is obtained using (8) multiplied by λ/(4π).
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Fig. 5.
Amplitude L-band SAR Image.
IV. R ESULTS Fig. 5 shows the amplitude image, at L-band, from a scene of a mountain area located in south Germany. The data for this scene were acquired in April 16 and Mai 25, 2004 (temporal baseline of 1 month and 9 days) with the purpose to identify possible landslide areas. The topography of the region varies from 550-1300m. Fig. 6 shows its differential interferograms (with wrapped phase). Fig. 6(a) is obtained without using PTA-MoComp. To generate this differential interferogram, it was necessary to unwrap the short-term residual inteferogram before phase scaling since its phase is greater then a phase cycle due to uncompensated motion errors. Fig. 6(a) shows that without topgraphy- and aperture-dependent MoComp, airborne D-InSAR becomes impracticable in mountain areas. Fig. 6(b) shows the differential interferogram obtained using PTA-MoComp. Now, there was no need of phase unwraping before phase scaling since the short-term residual interferogram phase is limited to a phase cycle. Fig. 6(b) shows a more reasonable D-INSAR result, although there seems to be residual motion errors in the image. By estimating the residual motion errors applying the multisquint approach, we expect improvements in the differential interferogram of Fig. 6(b). However further investigation to evaluate and interpret the remaining phase artefacts in the final differential interferogram is still in progress. V. C ONCLUSION In this paper we presented the required processing steps and the latest E-SAR processing chain to obtain sub-wavelength differential interferogram from airborne data. We showed differential inteferograms processed with the presented D-InSAR prossesing chain and the comparison of D-InSAR results when one of the steps of the proposed processing chain is missing. Since significant deviations from the nominal track in airborne case may always occur, we conclude that an accurate DEM (less then 10m accuracy) is needed throughout the whole process. We conclude also that after topography- and aperturedependent MoComp a step to estimate the residual motion errors is needed since there always exist a limit of accuracy in the navigation data. 0-7803-9050-4/05/$20.00 ©2005 IEEE.
Fig. 6. a) Differential interferogram without applying PTA-MoComp, b) applying PTA-MoComp. Coherence less then 0.3 are masked out (black regions).
ACKNOWLEDGMENT The authors would like to thank Andreas Reigber and Pau Prats for useful discussions. K.A.C. de Macedo holds a grant from CAPES, Brazil. R EFERENCES [1] A. Ferretti, C. Prati, and F. Rocca, ”Permanent Scatterers in SAR Interferometry”, IEEE Trans. on Geosc. and Rem. Sensing, Vol. 39, No. 1, pp. 8-20, 2001. [2] O. Mora, J. Mallorqui, and A. Broquetas, ”Linear and Nonlinear Terrain Deformation Maps from a Reduced Set of interferometric SAR Images”, IEEE Trans. on Geosc. and Rem. Sensing, Vol. 41, No. 10, pp. 2243-2253, 2003. [3] A. Moreira and Y. Huang, ”Airborne SAR Processing of Highly Squinted Data Using a Chirp Scaling Approach with Integrated Motion Compensation”, IEEE Trans. Geosci. and Remote Sensing, Vol. 32, No. 5, pp. 1029-1040, Sept. 1994. [4] P. Prats, A. Reigber, and J.J. Mallorqui, ”Interpolation-Free Coregistration and Phase-Correction of Airborne SAR Interferograms”, IEEE Geosci. and Remote Sensing Lett., Vol. 1, No. 3, pp. 188-191, Jul. 2004. [5] P. Prats, A. Reigber, and J.J. Mallorqui, ”Topography-Dependent Motion Compensation for Repeat-Pass Interferometric SAR Systems”, IEEE Geosci. and Remote Sensing Lett., Vol. 2, No. 2, pp. 206-210, Apr. 2005. [6] K.A.C. de Macedo, and R. Scheiber, ”Precise Topography- and ApertureDependent Motion Compensation for Airborne SAR”, IEEE Geosci. and Remote Sensing Lett., Vol. 2, No. 2, pp. 172-176, Apr. 2005. [7] D.E. Wahl, P.H. Eichel, D.C. Ghiglia, and C.V. Jakowatz, ”Phasegradient autofocus - A robust tool for high Resolution SAR phase correction”, IEEE Trans. Aerosp. and Electron. Syst., Vol. 30, No. 3, pp. 827-834, Jul. 1994 [8] R. Scheiber, A. Moreira ”Coregistration of interferometric SAR images using spectral diversity” IEEE Trans. on Geosci. and Remote Sens., Vol. 38, pp 2179-2191, Sep. 2000 [9] H.A. Zebker, P.A. Rosen, R.M Goldstein, A. Gabriel, and C. Werner ”On the derivation of coseismic displacement fields using differential radar interferometry: The Landers earthquake”, Journal of Geophysical Research, vol. 99, No. B10, pp. 19, 617-19, 634, 1994. [10] K.A.C. de Macedo, and R. Scheiber, ”Controlled Experiment for Analysis of Airborne D-InSAR Fesibility”, Proc. EUSAR’04, Ulm, Germany, May, 2004.
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Abstract— Airborne Differential SAR Interferometry (DInSAR) is still a challenging task when compared to the spaceborne case due to the fact that airborne platforms are unable to describe a stable flight track. For that reason a very precise motion compensation which includes the correction of topographic-induced phase errors has to be performed in the airborne SAR data. This paper presents the required steps of phase correction to achieve accurate airborne D-InSAR data. The latest airborne D-InSAR processing chain of the E-SAR system is shown. Differential interferograms results using the proposed processing chain are also shown.
I. I NTRODUCTION Differential Interferometry using Synthetic Aperture Radar, D-InSAR, is a technique to measure movements of the Earth’s surface at sub-wavelength scale. The D-InSAR technique uses the interferometric phases to measure the changes in the pathlength between two acquisition times. The interferometric phase between two SAR images taken at different times and from different positions can be expressed as (repeat-pass interferometry): φint = φtopo + φf e + φdif f ,
(1)
where φtopo denotes the phase contribution caused by terrain topography, φf e the systematic phase corresponding to the flat Earth, and φdif f the differential phase corresponding to the changes of the path-length. The differential phase, φdif f , is estimated by compensating the phase contributions due to topography and flat Earth by using a DEM (Digital Elevation Model)or/and a second interferometric phase without differential effect (very short temporal baseline). The accuracy of the D-InSAR measurements, φdif f , can be affected by atmospheric conditions, deviations of the platform from the nominal track, and noise contributions due to low SNR, baseline and temporal decorrelations. The Differential phase can be writen as: φdif f = φn + φatm + φ∆topo + φ∆dev ,
(2)
where φn denotes the noise contribution φatm the phase contribution due to changes in atmospheric conditions, φ∆topo the phase changes in the path length due to the changes of the terrain surface, and φ∆dev the difference between the phase errors due to the different deviations of the sensor at different acquisition times. 0-7803-9050-4/05/$20.00 ©2005 IEEE.
Using space-borne SAR sensors, differential interferometry with sub-wavelength accuracy can be achieved [1], [2]. Although often very efficient due to the very stable platform track, the use of space-borne SAR has some drawbacks like phase artefacts caused by atmospheric effects, and low coherent data due to long time acquisition intervals. Due to the great flexibility of airborne sensors, temporal decorrelations can be kept in reasonable levels by using small temporal baselines. The effects caused by the atmosphere is small because of the fact that the area imaged by the airborne radar signal is small and no significant variations of the atmosphere take place. For airborne case the accuracy of the D-InSAR measurements are mainly affected by the deviations of the platform from the nominal track. These deviations cause phase errors in the SAR image making airborne D-InSAR very difficult. Efforts to make airborne D-InSAR measurements efficient and accurate have been made in the past years, with the accuracy improvement of the navigation systems and motion compensation (MoComp) approaches [3], [4], [5], [6]. This paper describes the required steps and their importance in order to perform airborne differential interferometry. In section II, the paper explains briefly the origin and effects of phase errors due to motion deviations. In section III, the paper presents the required steps for differential interferometry together with the latest airborne D-InSAR processing chain of the E-SAR system. Section IV shows the differential inteferometry results obtained using the presented processing chain. In section V, we address the conclusions. II. O RIGIN AND E FFECTS OF P HASE E RRORS DUE TO M OTION D EVIATIONS The SAR raw data are processed as if they were acquired on straight rectilinear tracks. This assumption is not met with airborne platform as motion deviations (motion errors) of the sensor platform from the rectilinear (nominal) track can occur, causing phase errors both in range and azimuth. For a single SAR acquisition, the phase error due to these deviations, φdev , is proportional to the difference between the nominal and real path-length distance ∆r: 4π φdev = ∆r, (3) λ where λ is the wavelength of the radar signal.
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Fig. 2.
Fig. 1.
D-InSAR processing chain.
The phase error φdev is topography- and aperture-dependent [6]. In broadside direction (zero Doppler) φdev0 , is given by: 4π (h + ∆z)2 + ( r02 − h2 + ∆y)2 , (4) φdev0 (r, x, h) = λ where h is the target height, ∆r0 is the difference between the nominal and real path-length in broadside direction, r0 is the closest range between the SAR and the target, ∆y and ∆z are the deviations in the horizontal and in the vertical directions obtained from navigation system measurements, and r and x are the variables for range and azimuth positions respectively. The effects of motion errors are summarized in [6] A non-linear phase error causes phase offset (first order effect), shift of the SAR impulse response function (IRF) from the nominal position (second order effect) and defocusing (high order effects). For airborne differential SAR interferometry (repeat-pass) processing, a very accurate motion compensation, along the whole synthetic aperture, to correct the phase of each single pass data is neeed. This is because the deviations of two acquisition times may significantly differ causing mismatch and phase error in the repeat-pass interferograms. Using very precise motion compensation, the phase errors in a SAR image can be corrected to the level of accuracy of the navigation system and the external DEM used. The remaining (residual) motion error can be estimated using approaches as described in [4], [7]. The next section shows the required steps and the latest approaches of phase correction to achieve airborne D-InSAR data with sub-wavelength accuracy. Fig. 1 shows the block diagram for the D-InSAR processing chain. III. A IRBORNE D-I N SAR P ROCESSING C HAIN A. Motion Compensation The first requirement towards accurate D-InSAR data is to compensate all motion errors that are computable for each single data acquisition. As described in section II, the phase error is topography-dependent and due to the large variations 0-7803-9050-4/05/$20.00 ©2005 IEEE.
Phase error as function of the topography variation.
of incidence angle in airborne geometry, the MoComp approach for airborne SAR must correct the phase error taking into consideration the DEM of the imaged scene. Fig. 2 shows, for L-band, that difference of 10 meters or more between the height and the DEM used can introduce phase errors up to a 100 degrees for 10m deviation. To perform motion compensation of phase errors, the processing chain of the E-SAR airborne system first compensates the phase error assuming a flat terrain. This is performed within Extended Chirp Scaling (ECS) algorithm in a two step process [3]. Rough range invariant compensation is performed at raw data stage, whereas precise range dependent MoComp is included after RCMC (range cell migration correction) just prior to azimuth compression. This compensation methodology is very precise for flat terrain and for resolutions in the order of one meter. The previous approach is unable to perform a Topographyand Aperture-Dependent Motion Compensation due to the superposition of the synthetic aperture of several targets having different topographic heights. Thus, after the previous compensation, the topography- and aperture-dependent phase errors must be computed using a DEM. This remaining (or residual) phase error is then corrected using the so called PTA-MoComp (Precise Topography- and Aperture-Dependent Motion Compensation) [6]. The PTA-MoComp approach is a FFT-based post-processing algorithm capable of compensating the high-order effects due to the topography and due to the angular-variation (Dopplervariation) along the synthetic aperture. The resulting motion compensation after applying PTA-MoComp is very precise. The limit relies on the accuracy of the adopted navigation system and the DEM used. B. Residual Motion Errors Estimation and Compensation Due to the limit of accuracy of the adopted navigation system, there are still phase errors in the image that we are not able to compute. These residual motion errors shall be estimated. Let φres1 and φres2 be the phase contribution for the residual motion errors of two SAR images. For the ESAR navigation system, measurement errors in the order of centimeters are expected, leading up to hundreds of degrees of phase errors in L-Band. The method used to estimate residual motion errors in the ESAR airborne repeat-pass (differential interferometry) data is based on the multisquint approach [4]. This method estimates
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Fig. 3.
Estimated ∆φres phase error.
Fig. 4. Differential Equation Error as function of the topography variation (independent of wavelength).
the phase difference ∆φres between φres1 and φres2 , i.e. the residual motion errors in the interferogram. The ∆φres can be estimated by splitting the bandwidth of two SAR complex images S1 , S2 , building the interferograms of each subaperture A and B, and integrating their difference phase [4], [8]. The estimated ∆φres is then given by: ∆φres = arg [S1A S2A∗ (S1B S2B∗ )∗ ]dx + C, (5) where C is a unknown constant. The estimated ∆φres phase error can be converted into baseline deviations according to (right side-look geometry): λ = ∆By · cos (D ) − ∆Bz · sin (D ) , (6) 4π where D denotes the incidence angle, ∆By and ∆Bz the baseline errors in horizontal and vertical direction. Since the above method estimates the difference from the residual phase errors, we compensate the D-InSAR data by subtracting from the short- and long-term interferograms their corresponding estimated ∆φres phase error, followed by a pixel-by-pixel coregistration of the interferograms. Fig. 3 shows the estimated phase error ∆φres for the shortand long-term interferograms at near- and far-range for the D-InSAR data that will be shown in section IV. Due to the unknown constant in (5), an unknown baseline offset is presented in the interferometric data. Thus, a phase trend in range is to be expected. To compensate for this effect we compute the residual short- amd long-term interferograms, i.e., the short- and long-term inteferograms minus the interferometric phase derived from the DEM. Then, we take the range profiles of each residual interferograms and fit them to a quadratic function. The obtained phase trend is then inserted in (6) and the baseline offsets for each inteferogram are estimated in a least square sense. ∆φres
C. Generation of Differential Interferograms Even for ideal motion compensation or SAR images free of phase errors, special care has to be taken in order to generate airborne differential interferograms. The standard phase scaling approach to estimate the differential phase is given by [9]: Bl cos(θ0 − αl ) φints , φˆdif f,0 = φintl − Bs cos(θ0 − αs ) 0-7803-9050-4/05/$20.00 ©2005 IEEE.
(7)
where φints is the unwrapped short-term interferogram, φintl is the unwrapped long-term interferogram, αs is the tilt angle of the baseline for the short-term interferogram, αl is the tilt angle of the baseline for the long-term interferogram, Bs is the baseline length for the short-term interferogram, Bl is the baseline length for the long-term interferogram, θ0 is the look angle for the flat Earth. Due to the first order approximation around the look angle for the flat Earth involved in the derivation of (7), an error will appear when θ0 deviates from the real look angle, θtopo , which depends on the topography. For airborne geometry, the assumption of flat Earth during phase scaling leads to significant errors. Thus, the topography information must also be used to compute the airborne differential interferograms. Fig. 4 shows the error involved in the differential equation as a function of the topography. To obtain more accurate differential interferograms free of such phase errors, [10] reformulates the phase scaling and subtraction approach using an external DEM and 3 SAR data acquisition to form the short- and long-term interferograms. The estimation of the differential phase becomes [10]: Bl cos(θtopo − αl ) φresints , φˆdif f,topo = φresintl − Bs cos(θtopo − αs )
(8)
where φresints is the unwrapped residual short-term interferogram, φresintl is the unwrapped residual long-term interferogram θtopo is the look angle as function of the DEM. The differential interferograms of the E-SAR system are generated using (8). The error of the differential equation will be limited to the accuracy of the DEM used, which is is now the reference level in a pixel-by-pixel basis. In Fig. 4, we see that a 20m accurate DEM is enough for differential equation error lower than 1.0mm with 5m baseline interferograms. The phase of the residual interfrograms have mainly the contributions due to the surface movement, DEM error noise due to decorrelation effects and residual phase errors. If these contributions are negligible and the residual short-term interferogram phase φresint1 is limited to a phase cycle [−π, π) then, there is no need of unwrapping prior to phase scaling. The displacement map of the surface is obtained using (8) multiplied by λ/(4π).
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Fig. 5.
Amplitude L-band SAR Image.
IV. R ESULTS Fig. 5 shows the amplitude image, at L-band, from a scene of a mountain area located in south Germany. The data for this scene were acquired in April 16 and Mai 25, 2004 (temporal baseline of 1 month and 9 days) with the purpose to identify possible landslide areas. The topography of the region varies from 550-1300m. Fig. 6 shows its differential interferograms (with wrapped phase). Fig. 6(a) is obtained without using PTA-MoComp. To generate this differential interferogram, it was necessary to unwrap the short-term residual inteferogram before phase scaling since its phase is greater then a phase cycle due to uncompensated motion errors. Fig. 6(a) shows that without topgraphy- and aperture-dependent MoComp, airborne D-InSAR becomes impracticable in mountain areas. Fig. 6(b) shows the differential interferogram obtained using PTA-MoComp. Now, there was no need of phase unwraping before phase scaling since the short-term residual interferogram phase is limited to a phase cycle. Fig. 6(b) shows a more reasonable D-INSAR result, although there seems to be residual motion errors in the image. By estimating the residual motion errors applying the multisquint approach, we expect improvements in the differential interferogram of Fig. 6(b). However further investigation to evaluate and interpret the remaining phase artefacts in the final differential interferogram is still in progress. V. C ONCLUSION In this paper we presented the required processing steps and the latest E-SAR processing chain to obtain sub-wavelength differential interferogram from airborne data. We showed differential inteferograms processed with the presented D-InSAR prossesing chain and the comparison of D-InSAR results when one of the steps of the proposed processing chain is missing. Since significant deviations from the nominal track in airborne case may always occur, we conclude that an accurate DEM (less then 10m accuracy) is needed throughout the whole process. We conclude also that after topography- and aperturedependent MoComp a step to estimate the residual motion errors is needed since there always exist a limit of accuracy in the navigation data. 0-7803-9050-4/05/$20.00 ©2005 IEEE.
Fig. 6. a) Differential interferogram without applying PTA-MoComp, b) applying PTA-MoComp. Coherence less then 0.3 are masked out (black regions).
ACKNOWLEDGMENT The authors would like to thank Andreas Reigber and Pau Prats for useful discussions. K.A.C. de Macedo holds a grant from CAPES, Brazil. R EFERENCES [1] A. Ferretti, C. Prati, and F. Rocca, ”Permanent Scatterers in SAR Interferometry”, IEEE Trans. on Geosc. and Rem. Sensing, Vol. 39, No. 1, pp. 8-20, 2001. [2] O. Mora, J. Mallorqui, and A. Broquetas, ”Linear and Nonlinear Terrain Deformation Maps from a Reduced Set of interferometric SAR Images”, IEEE Trans. on Geosc. and Rem. Sensing, Vol. 41, No. 10, pp. 2243-2253, 2003. [3] A. Moreira and Y. Huang, ”Airborne SAR Processing of Highly Squinted Data Using a Chirp Scaling Approach with Integrated Motion Compensation”, IEEE Trans. Geosci. and Remote Sensing, Vol. 32, No. 5, pp. 1029-1040, Sept. 1994. [4] P. Prats, A. Reigber, and J.J. Mallorqui, ”Interpolation-Free Coregistration and Phase-Correction of Airborne SAR Interferograms”, IEEE Geosci. and Remote Sensing Lett., Vol. 1, No. 3, pp. 188-191, Jul. 2004. [5] P. Prats, A. Reigber, and J.J. Mallorqui, ”Topography-Dependent Motion Compensation for Repeat-Pass Interferometric SAR Systems”, IEEE Geosci. and Remote Sensing Lett., Vol. 2, No. 2, pp. 206-210, Apr. 2005. [6] K.A.C. de Macedo, and R. Scheiber, ”Precise Topography- and ApertureDependent Motion Compensation for Airborne SAR”, IEEE Geosci. and Remote Sensing Lett., Vol. 2, No. 2, pp. 172-176, Apr. 2005. [7] D.E. Wahl, P.H. Eichel, D.C. Ghiglia, and C.V. Jakowatz, ”Phasegradient autofocus - A robust tool for high Resolution SAR phase correction”, IEEE Trans. Aerosp. and Electron. Syst., Vol. 30, No. 3, pp. 827-834, Jul. 1994 [8] R. Scheiber, A. Moreira ”Coregistration of interferometric SAR images using spectral diversity” IEEE Trans. on Geosci. and Remote Sens., Vol. 38, pp 2179-2191, Sep. 2000 [9] H.A. Zebker, P.A. Rosen, R.M Goldstein, A. Gabriel, and C. Werner ”On the derivation of coseismic displacement fields using differential radar interferometry: The Landers earthquake”, Journal of Geophysical Research, vol. 99, No. B10, pp. 19, 617-19, 634, 1994. [10] K.A.C. de Macedo, and R. Scheiber, ”Controlled Experiment for Analysis of Airborne D-InSAR Fesibility”, Proc. EUSAR’04, Ulm, Germany, May, 2004.
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